Although we have already condensed our nebula to somewhere about 4,000,000 miles in diameter, where we have shown it might begin to radiate light--radiation of heat may have begun when the diameter was ten times as great, or even before that--we propose to return to the period when it had just abandoned the ring for the formation of Mercury and was 63,232,000 miles in diameter, and became what we have called the Solar nebula; because there is a good deal to be learned from a careful study of our operations up to that period, and of what must have taken place during further condensation up till the final establishment of the sun such as it is at the present time.
When the planet Neptune was discovered, Bode's Law fell into disrepute for a time, because the new planet was found to be much nearer to the sun than, according to it, it should have been. All the other planets occupied the places assigned to them within 5 per cent. of the exact appointed distance from the sun, but Neptune turned out to be 22·54 per cent. out of his exact place, and hence the discredit thrown upon the law. It was hard treatment for a servant that had helped so unmistakably--as we know to have been the case--to the discovery of the first four asteroids, which has afterwards been followed by the discovery of a whole host of them, and that had been pressed into the service for the discovery of the very planet which was the cause of its discredit--but such is the world. However, first offences against the law are generally looked upon with merciful eyes, and the Series of Titius seems to have been so far received into favour again that, some astronomers are said to have been looking out for another planet farther off than Neptune, being convinced that there must be some reason why a law that has shown itself to be right in eight cases should be altogether wrong in the ninth. Here, we think that the most likely explanation that can be given is, that the ring out of which Neptune was formed divided itself, after breaking up, into two planets instead of one, and that this is the reason why, Bode's Law could not point out the true position of either of them. It is hard enough to believe that the ring out of which Uranus was made--which we have seen may have been 954,000,000 miles broad, and over 3,400,000,000 miles in extreme diameter--could have united its fragments, after breaking up, into one planet, and the difficulty of belief becomes greater the greater the diameter comes to be. We have, in our work, considered the breadth of Neptune's ring to have been 1,010,000,000 miles, but then we limited the diameter of the nebula to 6,600,000,000 miles--we had to draw the line somewhere--whereas it may have been a thousand million miles greater, which would very greatly increase the probability of two planets, perhaps even more, having been formed out of the ring. If it has been so, the law could not apply to the case. A new Act was required. Besides, it is not a law, never has been, but only a register of facts; and we know that truths are often discovered from similar registers. It registers, and at the same time shows, that there is a nearly fixed inter-relation, even proportion, in the distances of the planets from the centre of the sun as far out as Uranus; and were we to make a similar register, beginning at the (present) outside of the planetary system, and registering the number of revolutions, beginning with 1 for Neptune, rates of acceleration of revolution in number of days, and densities of the planets, we may draw from it some useful knowledge. But we shall first extend Bode's Law to embrace Neptune, and show the discrepancies between the actual positions of the planets and those pointed out by the law.